Implementing typeful program transformations

Abstract

Abstract. The notion of program transformation is ubiquitous in programming language studies on interpreters, compilers, partial evaluators, etc. In order to implement a program transformation, we need to choose a representation in the meta language, that is, the programming language in which we construct programs, for representing object programs, that is, the programs in the object language on which the program transformation is to be performed. In practice, most representations chosen for typed object programs are typeless in the sense that the type of an object program cannot be reflected in the type of its representation. This is unsatisfactory as such typeless representations make it impossible to capture in the type system of the meta language various invariants in a program transformation that are related to the types of object programs. In this paper, we propose an approach to implementing program transformations that makes use of a first-order typeful program representation, where the type of an object program as well as the types of the free variables in the object program can be reflected in the type of the representation of the object program. We introduce some programming techniques needed to handle this typeful program representation, and then present an implementation of a CPS transform function where the relation between the type of an object program and that of its CPS transform is captured in the type system of DML. In a broader context, we claim to have taken a solid step along the line of research on constructing certifying compilers.

Finally tagless, partially evaluated: Tagless staged interpreters for simpler typed languages

“…In contrast, our CPS transformations use simpler types than GADTs and assure type preservation at the (terminating) type level rather than the term level of the metalanguage. Guillemette and Monnier review other type-preserving CPS transformations (mainly in the context of typed intermediate languages), in particular Shao et al's (2005) and Chen and Xi's (2003). These approaches use de Bruijn indices and fancier type systems with type-level functions, GADTs, or type-equality proofs.…”

A unified treatment of syntax with binders

“…In fact, dependent types can be used to encode not only the lexical scoping discipline, but also the type discipline of an object language: see, for instance, Chen and Xi (2003a;2003b) and Chlipala (2007). This is an aspect that we did not investigate and leave for future work.…”

A fresh look at programming with names and binders

“…In fact, dependent types can be used to encode not only the lexical scoping discipline, but also the type discipline of an object language: see, for instance, Chen and Xi [6] and Chlipala [7]. However, de Bruijn indices are, by nature, very low-level: it is desirable to build more abstract representations of top of them.…”